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After a quick review of the domain decomposition methods, and, more particularly on their application to large size problems relative to radiation and scattering of time-harmonic waves, we describe two contributions of the authors in this context. The two contributions are related to the scattering of a time-harmonic electromagnetic wave by a large perfectly conducting structure including a deep cavity. The first contribution is a substructuring technique. It is used to increase the speed of the convergence of the iterative algorithm in a Multi-Level Fast Multipol Method (MLFMM) solution. Numerical experiments illustrate the effectiveness of the approach since the number of iterations of the underlying Krylov iterative method remains almost constant while increasing a characteristic length in the problem. The second contribution proposes an adaptation of the overlapping domain decomposition techniques for a boundary integral formulation. It is used here to perform a hybridization of an exact formulation, used at the opening of the cavity, with an asymptotic high-frequency method employed for the rest of the exterior boundary of the structure. Numerical results demonstrate the reliability and the efficiency of the method.

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A novel Model Order Reduction (MOR) technique is developed to compute high-dimensional parametric solutions for electromagnetic fields in synchronous machines. Specifically, the intrusive version of the Proper Generalized Decomposition (PGD) is employed to simulate a Permanent-Magnet Synchronous Motor (PMSM). The result is a virtual chart allowing real-time evaluation of the magnetic vector potential as a function of the operation point of the motor, or even as a function of constructive parameters, such as the remanent flux in permanent magnets. Currently, these solutions are highly demanded by the industry, especially with the recent developments in the Electric Vehicle (EV). In this framework, standard discretization techniques require highly time-consuming simulations when analyzing, for instance, the noise and vibration in electric motors. The proposed approach is able to construct a virtual chart within a few minutes of off-line simulation, thanks to the use of a fully separated representation in which the solution is written from a series of functions of the space and parameters coordinates, with full space separation made possible by the use of an adapted geometrical mapping. Finally, excellent performances are reported when comparing the reduced-order model with the more standard and computationally costly Finite Element solutions.

In this paper a low noise flow duct facility that performs a multimodal characterization of the passive and active acoustic properties of obstacles in the aero-acoustic conditions of an automotive air conditioning system is presented. The experimental procedure is made of two steps. In the first one the passive data, i.e. the multimodal scattering matrix, is measured with a multi-sources method. In the second step the outgoing modal pressure spectra radiated upstream and downstream by the flow obstacle interaction source is achieved. A numerical simulation of the experiment based on a 3D-Finite Element Method is developed. A very good agreement between the theoretical and experimental results of the no flow scattering matrix of a diaphragm is found. The effect of the flow on the scattering matrix is shown before performing the measurement of the aero-acoustic source characteristics of the diaphragm.